Question 1184465
there are 20C4 ways to draw 4 balls=4845
one color
white is 7C4/20C4=35/4845 and may be reduced.
black is 5C4/20C4=5/4845
red is 6C4/20C4=15/4845
yellow is 0 since there must be at least 4 of them.
balls of 1 color has probability of 55/4845 of being drawn
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two colors would be 
(same denominator or 4845)
white black
7C1*5C3+7C2*5C2+7C3*5C1=70+210=175=455
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white red
7C1*6C3+7C2+6C2+7C3*6C1=140+315+210=665
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white-yellow
7C2*2C2+7C3+2C1=21+70=91
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black-red 
5C1*6C3+5C2*6C2+5C3*6C1=100+150+60=310
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black-yellow
5C2*2C2+5C3*2C1=30
-
red-yellow
6C2*2C2+6C3*2C1=55
Total for these is 1606/4845
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w-b-r
7C2*5C1*6C1+7C1*5C2*6C1+7C1*5C1*6C2=630+420+525=1575
w-b-y
7C2*5C1*2C1+7C1*5C2*2C1+7C1*5C1*2C2=210+140+35=385
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w-r-y
7C2*6C1*2C1+7C1*6C2*2C1+7C1*6C1*2C2=252+210+42=504
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b-r-y
5C2*6C1*2C1+5C1*6C2*2C1+5C1*6C1*2C2=120+150+30=300
That total is 2764/4845
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Not asked for but balls of 4 colors would be 7C2*5C1*6C1*2C1=420/4845

55+1606+2764+420=4845, and that accounts for all the possibilities.